Cartan's theorem

Cartan's theorem may refer to several mathematical results by Élie Cartan:

• Closed-subgroup theorem, 1930, that any closed subgroup of a Lie group is a Lie subgroup
• Theorem of the highest weight, that the irreducible representations of Lie algebras or Lie groups are classified by their highest weights
• Lie's third theorem, an equivalence between Lie algebras and simply-connected Lie groups

• Cartan's theorems A and B, c.1931 results by Henri Cartan concerning a coherent sheaf on a Stein manifold
• Cartan's lemma, several results by Élie or Henri Cartan
• Cartan–Dieudonné theorem, a result on orthogonal transformations and reflections